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1900's Physics and Wave

The ratio of ...

Question

The ratio of the radius difference between $4 t h$ and $3 r d$ orbit of H-atom and that of $L i^{2 +}$ ion is:

A

1 : 1

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B

3 : 1

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C

3 : 4

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D

9 : 1

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Solution

The correct option is B $3 : 1$
$r_{n} \propto \frac{v^{2}}{Z}; f o r H, r_{4} - r_{3} = 0.529 (16 - 9)$
$\Rightarrow 0.529 \times 7 ˚ A$
$r_{4} - r_{3}$ for $L i^{2 +} \Rightarrow 0.529 (\frac{16}{3} - \frac{9}{3})$
$\Rightarrow 0.529 \times \frac{7}{3}$ so ratio $\frac{7}{7 / 3} = 3 : 1$

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